This section provides background information related to the present disclosure which is not necessarily prior art. This section provides a general summary of the disclosure, and is not a comprehensive disclosure of its full scope or all of its features.
The present teachings provide an approach for minimizing tracking errors in dynamic systems (including those with non-minimum phase (NMP)) zeros by using filtered basis splines (B-splines). The output of the tracking controller is represented as a linear combination of B-splines having unknown coefficients. The basis functions are forward filtered using the dynamics of the system and their coefficients selected to minimize the errors in tracking a given trajectory. Among many other benefits, the use of B-splines allows: (i) constraints to be imposed on the input and outputs of the system as linear functions of the spline coefficients; (ii) non-zero initial conditions to be imposed; (iii) tracking of higher order derivatives; and (iv) the use of limited look ahead capabilities in the filtering process.
Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.
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